Sr Examen
Integral de t^(3/2)/(t^2+1) dx
Solución
Ha introducido
[src]
1 / | | 3/2 | t | ------ dt | 2 | t + 1 | / 0
$$\int\limits_{0}^{1} \frac{t^{\frac{3}{2}}}{t^{2} + 1}\, dt$$
Integral(t^(3/2)/(t^2 + 1), (t, 0, 1))
Respuesta (Indefinida)
[src]
/ | | 3/2 ___ / ___ ___\ ___ / ___ ___\ ___ / ___ ___\ ___ / ___ ___\ | t ___ \/ 2 *atan\1 + \/ 2 *\/ t / \/ 2 *atan\-1 + \/ 2 *\/ t / \/ 2 *log\4 + 4*t + 4*\/ 2 *\/ t / \/ 2 *log\4 + 4*t - 4*\/ 2 *\/ t / | ------ dt = C + 2*\/ t - --------------------------- - ---------------------------- - ---------------------------------- + ---------------------------------- | 2 2 2 4 4 | t + 1 | /
$$\int \frac{t^{\frac{3}{2}}}{t^{2} + 1}\, dt = C + 2 \sqrt{t} + \frac{\sqrt{2} \log{\left(- 4 \sqrt{2} \sqrt{t} + 4 t + 4 \right)}}{4} - \frac{\sqrt{2} \log{\left(4 \sqrt{2} \sqrt{t} + 4 t + 4 \right)}}{4} - \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{t} - 1 \right)}}{2} - \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{t} + 1 \right)}}{2}$$
Gráfica
Respuesta
[src]
___ ___ / ___\ ___ / ___\
pi*\/ 2 \/ 2 *log\8 + 4*\/ 2 / \/ 2 *log\8 - 4*\/ 2 /
2 - -------- - ---------------------- + ----------------------
4 4 4
$$- \frac{\sqrt{2} \pi}{4} - \frac{\sqrt{2} \log{\left(4 \sqrt{2} + 8 \right)}}{4} + \frac{\sqrt{2} \log{\left(8 - 4 \sqrt{2} \right)}}{4} + 2$$
=
=
___ ___ / ___\ ___ / ___\
pi*\/ 2 \/ 2 *log\8 + 4*\/ 2 / \/ 2 *log\8 - 4*\/ 2 /
2 - -------- - ---------------------- + ----------------------
4 4 4
$$- \frac{\sqrt{2} \pi}{4} - \frac{\sqrt{2} \log{\left(4 \sqrt{2} + 8 \right)}}{4} + \frac{\sqrt{2} \log{\left(8 - 4 \sqrt{2} \right)}}{4} + 2$$
2 - pi*sqrt(2)/4 - sqrt(2)*log(8 + 4*sqrt(2))/4 + sqrt(2)*log(8 - 4*sqrt(2))/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.